You really need to do some practice with interrupts. Your timing problem is easily fixed using a timer interrupt, your input problem also relies on handling your keyboard interrupt.

Write your algorithm down clearly, and decide at what points user inputs are needed. How do you cancel an action ? How do you start an action ? What bits cannot be interrupted, what can ?

LCD_INITIALISE
GAME INITIALISE
SHOW MESSAGE FOR START
WAIT FOR USER KEY
IF LEGAL KEY THEN PROCESS.
IF NOT LEGAL BEEP SOUNDER.

Write your algorithm in this pseudo-code form for a start , or draw a flow chart.

Steve